Free Access
Issue
ESAIM: COCV
Volume 22, Number 1, January-March 2016
Page(s) 112 - 133
DOI https://doi.org/10.1051/cocv/2014068
Published online 23 November 2015
  1. R.A. Adams, Sobolev Spaces. Academic Press, New York (1975). [Google Scholar]
  2. D.N. Arnold, J. Douglas and C.P. Gupta, A family of higher order mixed finite element methods for plane elasticity. Numer. Math. 45 (1984) 1–22. [CrossRef] [MathSciNet] [Google Scholar]
  3. D. Boffi, F. Brezzi and M. Fortin, Mixed Finite Element Methods and Applications. Springer, Heidelberg (2013). [Google Scholar]
  4. Z. Cai and G. Starke, First-order system least squares for the stress-displacement formulation: Linear elasticity. SIAM J. Numer. Anal. 41 (2003) 715–730. [CrossRef] [Google Scholar]
  5. Z. Cai and G. Starke, Least squares methods for linear elasticity. SIAM J. Numer. Anal. 42 (2004) 826–842. [CrossRef] [Google Scholar]
  6. Z. Cai and S. Zhang, Mixed methods for stationary Navier-Stokes equations based on pseudostress-pressure-velocity formulation. Math. Comput. 81 (2012) 1903–1927. [CrossRef] [Google Scholar]
  7. Z. Cai, B. Lee and P. Wang, Least squares methods for incompressible Newtonian fluid flow: Linear stationary problems. SIAM J. Numer. Anal. 42 (2004) 843–859. [CrossRef] [Google Scholar]
  8. Z. Cai, C. Tong, P.S. Vassilevski and C. Wang, Mixed finite element methods for incompressible flow: Stationary Stokes equations. Numer. Methods Partial Differ. Equ. 26 (2010) 957–978. [Google Scholar]
  9. C. Carstensen and G. Dolzmann, A posteriori error estimates for mixed FEM in elasticity. Numer. Math. 81 (1998) 187–209. [CrossRef] [MathSciNet] [Google Scholar]
  10. P.G. Ciarlet, On Korn’s inequality. Chin. Ann. Math. B 31 (2010) 607–618. [CrossRef] [MathSciNet] [Google Scholar]
  11. S. Dain, Generalized Korn’s inequality and conformal Killing vectors. Calc. Var. Partial Differ. Equ. 25 (2006) 535–540. [CrossRef] [Google Scholar]
  12. V.J. Ervin, J.S. Howell and I. Stanculescu, A dual-mixed approximation method for a three-field model of a nonlinear generalized Stokes problem. Comput. Methods Appl. Mech. Engrg. 197 (2008) 2886–2900. [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Fuchs and O. Schirra, An application of a new coercive inequality to variational problems studied in general relativity and in Cosserat elasticity giving the smoothness of minimizers. Arch. Math. (Basel) 93 (2009) 587–596. [CrossRef] [MathSciNet] [Google Scholar]
  14. M. Fuchs and S. Repin, Some Poincaré-type inequalities for functions of bounded deformation involving the deviatoric part of the symmetric gradient. Zap. Nauchn. sem. St.-Petersburg Odtel. Math. Inst. Steklov (POMI) 385 (2010) 224–234. [Google Scholar]
  15. G. Gatica, A. Márquez and M.A. Sánchez, Analysis of a velocity-pressure-pseudostress formulation for the stationary Stokes equations. Comput. Methods Appl. Mech. Engrg. 199 (2010) 1064–1079. [CrossRef] [MathSciNet] [Google Scholar]
  16. T. Jakab, I. Mitrea and M. Mitrea, On the regularity of differential forms satisfying mixed boundary conditions in a class of Lipschitz domains. Indiana Univ. Math. J. 58 (2009) 2043–2071. [CrossRef] [MathSciNet] [Google Scholar]
  17. F. Jochmann, A compactness result for vector fields with divergence and curl in Lq(Ω) involving mixed boundary conditions. Appl. Anal. 66 (1997) 189–203. [CrossRef] [Google Scholar]
  18. S. Münzenmaier, First-order system least squares for generalized-Newtonian coupled Stokes-Darcy flow. Numer. Methods Partial Differ. Equ. 31 (2015) 1150–1173. [CrossRef] [Google Scholar]
  19. S. Münzenmaier and G. Starke, First-order system least squares for coupled Stokes-Darcy flow. SIAM J. Numer. Anal. 49 (2011) 387–404. [CrossRef] [Google Scholar]
  20. J. Nečas, Sur les normes équivalentes dans Formula et sur la coercivité des formes formellement positives, in Équations aux derivées partielles. Les Presses de l’Université de Montréal (1967) 102–128. [Google Scholar]
  21. P. Neff and K. Chełmiński, Infinitesimal elastic-plastic Cosserat micropolar theory. Modelling and global existence in the rate independent case. Proc. Roy. Soc. Edinb. A 135 (2005) 1017–1039. [CrossRef] [Google Scholar]
  22. P. Neff and I. Münch, Curl bounds Grad on SO(3). ESAIM: COCV 14 (2008) 148–159. [CrossRef] [EDP Sciences] [Google Scholar]
  23. P. Neff and J. Jeong, A new paradigm: the linear isotropic Cosserat model with conformally invariant curvature energy. Z. Angew. Math. Mech. 89 (2009) 107–122. [CrossRef] [Google Scholar]
  24. P. Neff, K. Chełmiński, W. Müller and C. Wieners, A numerical solution method for an infinitesimal elastic-plastic Cosserat model. M3AS Math. Mod. Meth. Appl. Sci. 17 (2007) 1211–1239. [CrossRef] [Google Scholar]
  25. P. Neff, K. Chełmiński and H.D. Alber, Notes on strain gradient plasticity. Finite strain covariant modelling and global existence in the infinitesimal rate-independent case. M3AS Math. Mod. Meth. Appl. Sci. 19 (2009) 1–40. [CrossRef] [Google Scholar]
  26. P. Neff, D. Pauly and K.J. Witsch, On a canonical extension of Korn’s first inequality to H(Curl) motivated by gradient plasticity with plastic spin. C. R. Math. 349 (2011) 1251–1254. [CrossRef] [Google Scholar]
  27. P. Neff, D. Pauly and K.J. Witsch, Maxwell meets Korn: a new coercive inequality for tensor fields in RN × N with square-integrable exterior derivative. Math. Methods Appl. Sci. 35 (2012) 65–71. [CrossRef] [Google Scholar]
  28. P. Neff, I.D. Ghiba, A. Madeo, L. Placidi and G. Rosi, A unifying perspective: the relaxed linear micromorphic continuum. Cont. Mech. Thermodyn. 26 (2014) 639–681. [CrossRef] [Google Scholar]
  29. P. Neff, D. Pauly and K.J. Witsch, Poincaré meets Korn via Maxwell: Extending Korn’s first inequality to incompatible tensor fields. J. Differ. Equ. 258 (2015) 1267–1302. [CrossRef] [Google Scholar]
  30. W. Pompe, Counterexamples to Korn’s inequality with non-constant rotation coefficients. Math. Mech. Solids 16 (2011) 172–176. [CrossRef] [Google Scholar]
  31. Y.G. Reshetnyak, Stability Theorems in Geometry and Analysis. Kluwer Academic Publishers, London (1994). [Google Scholar]
  32. O. Schirra, New Korn-type inequalities and regularity of solutions to linear elliptic systems and anisotropic variational problems involving the trace-free part of the symmetric gradient. Calc. Var. Partial Differ. Equ. 43 (2012) 147–172. [CrossRef] [Google Scholar]
  33. H. Sohr, The Navier−Stokes Equations. Birkhäuser, Basel (2001). [Google Scholar]
  34. K. Yoshida, Functional Analysis. Springer-Verlag, Berlin, 6th edition (1980). [Google Scholar]

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